Question: Simplify the following expression: $\sqrt{7}+\sqrt{175}-\sqrt{112}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{7}+\sqrt{175}-\sqrt{112}$ $= \sqrt{7}+\sqrt{25 \cdot 7}-\sqrt{16 \cdot 7}$ Separate the radicals and simplify. $= \sqrt{7}+\sqrt{25} \cdot \sqrt{7}-\sqrt{16} \cdot \sqrt{7}$ $= \sqrt{7}+5\sqrt{7}-4\sqrt{7}$ Finally, simplify by combining the terms. $= ( 1 + 5 - 4 )\sqrt{7} = 2\sqrt{7}$